Schrödinger type propagators, pseudodifferential operators and modulation spaces

Abstract

We prove continuity results for Fourier integral operators with symbols in modulation spaces, acting between modulation spaces. The phase functions belong to a class of nondegenerate generalized quadratic forms that includes Schrödinger propagators and pseudodifferential operators. As a byproduct we obtain a characterization of all exponents $p,q,r_1,r_2,t_1,t_2\in [1,\infty ]$ of modulation spaces such that a symbol in $M^{p,q}({\mathbb{R}}^{2d})$ gives a pseudodifferential operator that is continuous from $M^{r_1,r_2}({\mathbb{R}}^d)$ into $M^{t_1,t_2}({\mathbb{R}}^d)$.

25 pages, 2 figures, to appear in J. London Math. Soc

References in corpus (2)

• Global L2-boundedness theorems for a class of Fourier integral operators
• The Wiener Property for a Class of Fourier Integral Operators

Cited by in corpus (5)

• Sharp integral bounds for Wigner distributions
• Time-frequency Analysis of Born-Jordan Pseudodifferential Operators
• Norm Estimates for $\tau$-Pseudodifferential Operators in Wiener Amalgam and Modulation Spaces
• Boundedness of Pseudodifferential Operators with symbols in Wiener amalgam spaces on Modulation Spaces
• On $L^p-$boundedness of pseudo-differential operators of Sjöstrand's class